This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001795 M4407 N1861 #47 Apr 23 2025 04:50:17
%S A001795 1,1,7,33,715,4199,52003,334305,17678835,119409675,1641030105,
%T A001795 11435320455,322476036831,2295919134019,32968493968795,
%U A001795 238436656380769,27767032438524099,203236010537432691,2989949596465113373
%N A001795 Coefficients of Legendre polynomials.
%C A001795 Numerators in expansion of sqrt(c(x)), c(x) the g.f. of A000108. - _Paul Barry_, Jul 12 2005
%C A001795 Coefficient of Legendre_0(x) when x^n is written in term of Legendre polynomials. - _Michel Marcus_, May 28 2013
%D A001795 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001795 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001795 T. D. Noe, <a href="/A001795/b001795.txt">Table of n, a(n) for n = 0..100</a>
%H A001795 H. E. Salzer, <a href="http://dx.doi.org/10.1090/S0025-5718-1948-0023123-5">Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials</a>, Math. Comp., 3 (1948), 16-18.
%F A001795 1/(sqrt(1-x) + sqrt(1+x)) = Sum_{n>=0} (a(n)/b(n))*x^(2*n) where b(n) is a power of 2. - _Benoit Cloitre_, Mar 12 2002
%F A001795 For n >= 1, 2^(n+1)*a(2^(n-1)) = A001791(2^n). - _Vladimir Shevelev_, Sep 05 2010
%F A001795 a(n) = numerator(binomial(2*n-1/2, n)/(2*n+1)). - _Tani Akinari_, Oct 22 2024
%F A001795 a(n) = numerator( A000108(2*n)/4^n ). - _G. C. Greubel_, Apr 22 2025
%t A001795 Table[Numerator[CatalanNumber[2*n]/4^n], {n,0,30}] (* _G. C. Greubel_, Apr 22 2025 *)
%o A001795 (PARI) my(x='x+O('x^30)); apply(numerator, Vec(((1-sqrt(1-4*x))/(2*x))^(1/2))) \\ _Michel Marcus_, Feb 04 2022
%o A001795 (PARI) a(n)=numerator(binomial(2*n-1/2, n)/(2*n+1)) \\ _Tani Akinari_, Oct 22 2024
%o A001795 (Magma)
%o A001795 A001795:= func< n | Numerator(Catalan(2*n)/4^n) >;
%o A001795 [A001795(n): n in [0..25]]; // _G. C. Greubel_, Apr 22 2025
%o A001795 (SageMath)
%o A001795 def A001795(n): return numerator(catalan_number(2*n)/4^n)
%o A001795 print([A001795(n) for n in range(31)]) # _G. C. Greubel_, Apr 22 2025
%Y A001795 Divisor of A048990 and A065097.
%Y A001795 Apparently a bisection of A002596.
%Y A001795 Bisection of A099024.
%Y A001795 Cf. A000108, A001791.
%K A001795 nonn
%O A001795 0,3
%A A001795 _N. J. A. Sloane_
%E A001795 More terms from _Benoit Cloitre_, Mar 12 2002